Molière's Theory of Multiple Scattering

Mole\`ere's theory of multiple scattering of electrons and other charged particles is here derived in a mathematically simpler way. The differential scattering law enters the theory only through a single parameter, the screening angle {₀}^', Eq. (21). The angular distribution, except for the absolute scale of angles, depends again only on a single parameter b, Eq. (22). It is shown that b depends essentially only on the thickness of the scattering foil in g/cm^2, and is nearly independent of Z. The transition to single scattering is re-investigated. An asymptotic formula is obtained which agrees essentially with that of Moli\`ere, Snyder, and Scott, but which remains accurate down to smaller angles, Eq. (38). The theory of Goudsmit and Saunderson has a close quantitative relation to that of Moli\`ere, and a good approximation to their distribution function can be obtained by multiplying Moli\`ere's function by (sin). This relation holds until the scattering angles become so large that only very few terms in the series of Goudsmit and Saunderson need to be taken into account.